I agree with deschain, building muscle is very important for fat loss.
I would try to focus more on building up your muscles and a little less on cardio. Although you can always be like me and mix them up
As for the whole "which comes first" - I would put the weightlifting in front of cardio, especially in your case since you said you go light on the lifting.
If you do your cardio first, you'll have no energy to put into lifting.
However, if you do some light lifting first, you'll still have plenty of energy left for cardio.
Or you can even consider, like I mentioned earlier, mixing them together. However, if you do that you won't be doing "traditional" cardio, which is boring anyway.
For a quick example, you could do a set of bench pressing, then immediately do 10-15 vertical leaps, mountain climbers, jumping lunges, etc.
Then go back and do another set of benching, then another set for legs/endurance.
That's the kind of thing I like to do. It keeps it much more interesting and tests out your mental toughness big time. I just don't lift weights anymore, that's all. I do
mostly bodyweight movements that I think are a lot better anyway.